Baylor Engineering, Math Collaboration Receives New Funding

Three Baylor University researchers, one of the only interdisciplinary groups in the world investigating the engineering applications of time scale mathematics, have received a new research grant from the National Science Foundation to study dynamic equations on self-generating time domains.

The research addresses an increasingly relevant problem as computers become more numerous in everyday objects like cars, toys, electronics and appliances. When engineers design one of those objects, they must overcome a fundamental mismatch between "computer time" and real time. Computers work only at distinct points in time, while the physical world advances in continuous time. The marrying of these two results in a system that shows behavior that is neither discrete nor continuous in the usual senses. Thus, the system generates its own time domain. The research investigates how to apply the mathematical field of dynamic equations on time scales to model these types of different systems.

To conduct the project, each of the three researchers will bring a unique set of skills to the table. Dr. John Davis, an associate professor of mathematics at Baylor, is the group's leading expert in mathematics of time scales. Dr. Robert Marks, distinguished professor of electrical and computer engineering at Baylor, acts as the "idea" researcher by providing insight and a general strategy on making the mathematics useful for engineers. Dr. Ian Gravagne, an assistant professor of electrical and computer engineering at Baylor and the lead researcher on the project, applies the mathematics to engineering problems like high-gain adaptive control and controller-area-network bandwidth optimization.

The research comes on the heels of a related NSF grant the group received three years ago that aimed to use time scale mathematics to improve the design of distributed control networks. While doing that work, the researchers realized there was a gap in the understanding of dynamic equations on self-generating time domains.

"This may sound odd, but we now understand more about what we don't understand, so the problems we are tackling are better defined and more focused now," Gravagne said. "The overall goal is to keep the cost down of building a given network even as more functionality is added to the network."